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Properties

Label 3850.2.ff
Level $3850$
Weight $2$
Character orbit 3850.ff
Rep. character $\chi_{3850}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1920$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3850.ff (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1925 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3850, [\chi])\).

Total New Old
Modular forms 5824 1920 3904
Cusp forms 5696 1920 3776
Eisenstein series 128 0 128

Trace form

\( 1920 q + 240 q^{4} + 12 q^{5} - 10 q^{7} + 240 q^{9} + O(q^{10}) \) \( 1920 q + 240 q^{4} + 12 q^{5} - 10 q^{7} + 240 q^{9} + 4 q^{11} - 8 q^{15} + 240 q^{16} - 20 q^{22} + 10 q^{23} + 10 q^{25} - 20 q^{28} + 36 q^{31} + 120 q^{33} + 50 q^{35} - 480 q^{36} + 50 q^{39} + 200 q^{43} + 4 q^{44} - 12 q^{45} + 20 q^{46} + 38 q^{49} - 80 q^{50} - 40 q^{57} + 4 q^{60} + 30 q^{61} - 60 q^{63} - 480 q^{64} - 70 q^{65} + 48 q^{66} + 64 q^{70} + 64 q^{71} + 60 q^{75} + 50 q^{77} + 18 q^{80} + 224 q^{81} - 60 q^{85} + 24 q^{86} + 20 q^{88} + 30 q^{89} + 64 q^{91} - 20 q^{92} + 80 q^{93} + 70 q^{95} + 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3850, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1925, [\chi])\)\(^{\oplus 2}\)